/*
`-:://:::-
`//:-------:/:`
.+:--.......--:+`
`+:--..`````..--//`
.o:--..`` ``..--:o`
.o:--...```..---+/`
`/y+o/---....---:+o.
`...````-os+/:---:/+o/--.`
`-/+++++/:. `...` :h+d+oooo+/+-` ...
`/++//:::://++-`....` -.`//````````:` `..`
`o+/::------://o/` `-` -. -` `..`
`---.-o/:./o/::-..``..-ЗАПУСКАЕМ .. .. -` `... ``..``
`....o+:-++/:--.```..-://s. `-` .- -` `-o: .-//::::/:-`
`:s+/:--....-::/+s-` .- `- -` -///:--------:/:`
./s+//:::::://oo-``..НЕЙРОННУЮ: СЕТЬ:::::::-`РАБОТЯГИ `+:--........--:/`
.:ooo+++++osso-` `.:-...`/` ./::-------:/:` -` :+--..``````.--:+:...-+:-`
`.-/+++++/+-.-` -. ``:so:/:--.......--:+` `-```````o+/+--..`````..--:o/-..:s+:.
```````:``.. `-` -` `+:--..`````..--/+-.../.`````..-o:--.......---/o. `
`: `:- -. .o:--..`` ``..--:o` `-` `:o+:--------:+o-`
`-`-... .. .o/--...```..--:+/` `-` `oy/so/////++o/.`
-/` `-` `- ``+s/o/:---...---:++. `-` .-../d://///:-.`
`.---..``-..- .-/..`````-oo+/:::::/+o+- `-``-` `-. ````
`:++++/+++++- ..``.-/:` /y-:/++o++/:.`..` ./. `-
-++/::::::://+/..:-``:` .. `-.` ```.``` `..` `..`-` `-
`` -o//:--....-::/++` -.-` `-`.-` `..`..` `-.-
-----ss+:++/:--.```..-://s. /. `:: `-:. ./`
`````/:..+o/::-..``.--:/+s. ..-` `-``-` ..` `-` `-`-`
`-s+/::-----::/+oo---``-` .. .:- ``` .-` .-.- `-`
`:oo+//::://+os/..:`..-/:` :y.-:::::::.`.-` ./-` `-`
`./+oooooooo+/.`- .-:...`.. .//:-------://` `- `..` `:.
``.-::::-.``-/` `-` `- `oo:+:--.......--:/` `- `.:--h.``..```
-.-`.- .- `+:--..`````..--//` `- /s-//::::::::.
-` `/- .. .o:--..`` ``..--:o.```.- `//:--------://`
-` .-`.-` -.`-o/--...```..--:+/.``-:....``:-.+:--....`...--:+`
..`-. `-. ``:os:o/:---...---:++. `- ``///+:-..``````.--:+-````-.`
`.:///////.-` .:-..` -``-+o+/:::::/+o/. `- `:+:-..`````..--:o/:--/ys+-
`-++///////+o/. ``....`-. :` `.:++++++/:.` .- -o/---......---/o. `.`
`++//:-----::/+o:..` .-` : ``````` .- `+so+:--------:++-`
`````:-``:o/::-..`..--:/+o` -. `- .- `../../+o+////+o+:.`
-----syo/o+/:--.```..-://s. .-` `- .- `... ``-:////:-``
.` `/s//:--....-::/+s. -. `-` .- `..`
.+o+/:::--:://+s/-..` .::+y ``` .- `..`
./oo++////+oso-` `.... :y-+:::::::/` ...
`.:+oooooo/-` `....-. .//:-------:/:-.`
``...`` /+:+:--.......--:+`
`+:--..`````..--//`
.o:--..`` ``..--:o`
.+/--...```..--:+/`
`-o/:---...---:++.
`-+o+/:---:/+o/.
`.:+oooo+/-.`
``````
*/
#ifdef aimbot
#pragma comment(linker, "/stack:200000000")
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#pragma GCC optimize("unroll-loops")
#endif
#define hur(f, g) template<class c> int f(c a) {if (sizeof(c) == 8) return g##ll(a); else return g(a);}
hur(popc, __builtin_popcount) hur(ctz, __builtin_ctz) hur(clz, __builtin_clz)
/*
- place bitset modifications here
*/
#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <map>
#include <set>
#include <queue>
#include <ostream>
#include <istream>
#include <typeinfo>
#include <iomanip>
#include <cstdio>
#include <cstdlib>
#include <cassert>
#include <limits>
#include <fstream>
#include <array>
#include <list>
#include <bitset>
#include <functional>
#include <random>
#include <cstring>
#include <chrono>
#define random escape__from__random__aetuhoetnuhshe
#define mt make_tuple
#define x first
#define y second
#define pb push_back
#define mp make_pair
#define le(v) ((int)v.size())
#define f(i, n) for (int i = 0; i < (n); i++)
#define rof(i, n) for (int i = ((n) - 1); i >= 0; i--)
#define apply(v, act) for (auto &x : v) { act; }
#define log(args...) {string s = #args;deque<string> deq;\
string buf = "";int bal = 0;for (char c : s) {\
if (c == '(' || c == '[' || c == '{') {bal++;\
} else if (c == ')' || c == ']' || c == '}') {\
bal--;} else {if (bal == 0) {if (c == ',') {\
deq.pb(buf);buf = "";} else {if (c != ' ') {\
buf += c;}}}}}if (!buf.empty()) {deq.pb(buf);}\
smart_io::precall_print();smart_io::_print(deq, args);}
inline int min(const int &x, const int &y) { return (((y-x)>>(32-1))&(x^y))^x; }
inline int max(const int &x, const int &y) { return (((y-x)>>(32-1))&(x^y))^y; }
inline long long min(const long long &x, const long long &y) { return (((y-x)>>(64-1))&(x^y))^x; }
inline long long max(const long long &x, const long long &y) { return (((y-x)>>(64-1))&(x^y))^y; }
#define print \
smart_io::precall_print(); \
cout,
#define scan cin,
#ifdef fast_allocator
const int MAXMEM = 200 * 1000 * 1024;
char _memory[MAXMEM];
size_t _ptr = 0;
void* operator new(size_t _x) { _ptr += _x; assert(_ptr < MAXMEM); return _memory + _ptr - _x; }
void operator delete (void*) noexcept {}
#endif
using namespace std;
char string_in_buffer[(int)260];
void fast_scan(int &x) { scanf("%d", &x); }
void fast_scan(long long &x) { scanf("%lld", &x); }
void fast_scan(unsigned long long &x) { scanf("%llu", &x); }
void fast_scan(double &x) { scanf("%lf", &x); }
void fast_scan(long double &x) { scanf("%Lf", &x); }
void fast_scan(char &x) {
scanf("%c", &x);
if (x == '\n') {
fast_scan(x);
}
}
void fast_scan(string &x) {
scanf("%s", string_in_buffer);
x = string(string_in_buffer);
}
template<class TFirst, class TSecond>
void fast_scan(pair<TFirst, TSecond> &p) {
fast_scan(p.first);
fast_scan(p.second);
}
template <class T>
void fast_scan(vector<T> &v) {
for (auto &x : v) fast_scan(x);
}
void fast_print(const int &x) { printf("%d", x); }
void fast_print(const unsigned int &x) { printf("%u", x); }
void fast_print(const long long &x) { printf("%lld", x); }
void fast_print(const unsigned long long &x) { printf("%llu", x); }
void fast_print(const char &x) { printf("%c", x); };
// void fast_print(__int128 x) {
// if (x == 0) { fast_print('0'); return; }
// if (x < 0) {
// fast_print('-');
// x = -x;
// }
// __int128 p = 1;
// while (x / (p * 10)) p *= 10;
// while (p) {
// __int128 symb = x / p;
// fast_print((int)symb);
// x -= p * symb;
// p /= 10;
// }
// };
void fast_print(const double &x) { printf("%.15lf", x); }
void fast_print(const long double &x) { printf("%.15Lf", x); }
void fast_print(const string &x) { printf("%s", x.c_str());}
void fast_print(const char v[]) { fast_print((string)v); }
template<class TFirst, class TSecond>
void fast_print(const pair<TFirst, TSecond> &p) {
fast_print(p.first);
fast_print(' ');
fast_print(p.second);
}
template <class T>
void fast_print(const vector<T> &v) {
if (v.empty()) return;
fast_print(v[0]);
for (int i = 1; i < v.size(); i++) {
fast_print(' ');
fast_print(v[i]);
}
}
template <class T>
void fast_print(const vector<vector<T>> &v) {
if (v.empty()) return;
fast_print(v[0]);
for (int i = 1; i < v.size(); i++) {
fast_print('\n');
fast_print(v[i]);
}
}
template <class T>
void fast_print(const T &v) {
for (const auto &x : v) {
fast_print(x);
fast_print(' ');
}
}
using namespace std;
namespace smart_io {
string print_start = "";
string sep = " ";
bool first_print = false;
void precall_print() {
fast_print(print_start);
print_start = "\n";
first_print = true;
}
void _print(deque<string>) {}
template<class T, class... Args>
void _print(deque<string> names, T elem, Args... args) {
if (!first_print) {
fast_print("\n");
} else {
first_print = false;
}
fast_print(names.front());
fast_print(" = ");
fast_print(elem);
names.pop_front();
_print(names, args...);
}
} //namespace smart_io
template <class T>
ostream &operator,(ostream &os, const T &object) {
if (!smart_io::first_print) {
fast_print(smart_io::sep);
} else {
smart_io::first_print = false;
}
fast_print(object);
return os;
}
template <class T>
istream &operator,(istream &is, T &object) {
fast_scan(object);
return is;
}
namespace random {
using namespace std::chrono;
mt19937 rng(duration_cast< milliseconds >(
system_clock::now().time_since_epoch()
).count());
uniform_real_distribution<> prob_dist(0.0, 1.0);
};
namespace typedefs {
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> pii;
typedef long double ld;
}
namespace numbers_operation {
template<class T>
inline T floor_mod(T a, const T &b) {
a %= b;
if (a < 0) a += b;
return a;
}
}
using namespace numbers_operation;
using namespace typedefs;
using namespace random;
const ll MOD = 1e9 + 7;
// const ll MOD = 998244353;
template<ll MOD>
struct Ring {
ll value = 0;
Ring() {}
Ring(int _value) {
value = _value;
value = floor_mod(value, MOD);
}
Ring(ll _value) {
value = _value;
value = floor_mod(value, MOD);
}
Ring pow(ll p) const {
Ring r = 1;
Ring x; x.value = value;
while (p) {
if (p & 1) r *= x;
x *= x;
p /= 2;
}
return r;
}
Ring inv() const {
return pow(MOD - 2);
}
void operator*=(const Ring<MOD> &b) {
value *= b.value;
value = floor_mod(value, MOD);
}
friend Ring operator*(Ring<MOD> a, const Ring<MOD> &b) {
a *= b;
return a;
}
void operator+=(const Ring<MOD> &b) {
value += b.value;
value -= (value >= MOD) * MOD;
}
friend Ring operator+(Ring a, const Ring &b) {
a += b;
return a;
}
void operator-=(const Ring<MOD> &b) {
value -= b.value;
value += (value < 0) ? MOD : 0;
}
friend Ring operator-(Ring a, const Ring &b) {
a -= b;
return a;
}
void operator/=(const Ring<MOD> &b) {
(*this) *= b.inv();
}
friend Ring operator/(Ring a, const Ring &b) {
a /= b;
return a;
}
bool operator==(const Ring<MOD> &b) {
return value == b.value;
}
bool operator!=(const Ring<MOD> &b) {
return value != b.value;
}
friend void fast_print(const Ring<MOD> &b) {
fast_print(b.value);
}
};
typedef Ring<MOD> num;
int n;
vector<bool> vis;
int mem_binom[150][150];
num binom(int n, int k) {
if (k > n) return 0;
if (n == 0 || k == 0) return 1;
if (mem_binom[n][k] != -1) return mem_binom[n][k];
mem_binom[n][k] = (binom(n - 1, k - 1) + binom(n - 1, k)).value;
return mem_binom[n][k];
}
int mem_place[150][150][150][2];
num place(int n, int places, int up, bool spec) {
if (places < 0) return 0;
if (n == 0) return (spec == true) && (up == 0);
if (spec && up == 0) return 0;
if (mem_place[n][places][up][spec] != -1)
return mem_place[n][places][up][spec];
// take from 0 to 2
num rez = 0;
f(t, min(3, places + 1)) {
if (t + up == 0) continue;
rez += binom(places, t)
* place(n - 1, places - t, up + t - 1, spec)
* (t == 0 ? num(2).inv() : 1);
// in case we left 2 elems for covering holes
}
if (!spec) {
f(t, min(3, places + 2)) {
if (t == 0) continue;
if (t + up == 0) continue;
num coef = 1;
if (t == 2) {
coef = places;
}
rez += coef
* place(n - 1, places - (t - 1), up + t - 1, true)
* (t == 0 ? num(2).inv() : 1);
// in case we left 2 elems for covering holes
}
}
mem_place[n][places][up][spec] = rez.value;
return rez;
}
int mem_dp[150][150];
num dp(int i, int j) {
if (i == -1) {
return j == n / 2 + 1;
}
if (mem_dp[i][j] != -1) return mem_dp[i][j];
/*
Assume we are standing at i
and current missing element is j
elements 1..j - 1 already in use
*/
num rez = 0;
if (!vis[i]) {
// that means that
// we put one of the hidden elements
int elems = j - 1;
for (int k = i + 1; k < n; k++) {
elems -= !vis[k];
}
// print j, "->", elems;
rez = dp(i - 1, j) * elems;
} else {
// remain unchanged
rez += dp(i - 1, j);
// bruteforce new height
int places = 0;
for (int it = i + 1; it < n; it++) {
places += vis[it];
}
places -= j - 1; // not engaged places
for (int k = j + 1; k <= n + 1; k++) {
// put elems j, j + 1, ..., k - 1
// on arbitrary vis positions
// if (i == n - 1) {
// print j, k, "?", k - j, places, 0, ":";
// print place(k - j, places, 0, false), dp(i - 1, k);
// }
rez += place(k - j, places, 0, false) * dp(i - 1, k);
}
}
mem_dp[i][j] = rez.value;
return rez;
}
signed main(signed argc, char *argv[]) {
memset(mem_dp, -1, sizeof mem_dp);
memset(mem_binom, -1, sizeof mem_binom);
memset(mem_place, -1, sizeof mem_place);
scan n;
n *= 2;
vis.resize(n);
f(i, n / 2) {
int x; scan x; x--; vis[x] = true;
}
// print place(1, 1, 0);
// print dp(n - 2, 1);
// print dp(n - 3, 1);
// print dp(n - 3, 2);
// print dp(n - 3, 3);
// print dp(n - 2, 2);
// print place(1, 0, 0, false);
print dp(n - 1, 1);
}
Compilation message
ruins3.cpp: In function 'void fast_scan(int&)':
ruins3.cpp:141:31: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
void fast_scan(int &x) { scanf("%d", &x); }
~~~~~^~~~~~~~~~
ruins3.cpp: In function 'void fast_scan(long long int&)':
ruins3.cpp:142:37: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
void fast_scan(long long &x) { scanf("%lld", &x); }
~~~~~^~~~~~~~~~~~
ruins3.cpp: In function 'void fast_scan(long long unsigned int&)':
ruins3.cpp:143:46: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
void fast_scan(unsigned long long &x) { scanf("%llu", &x); }
~~~~~^~~~~~~~~~~~
ruins3.cpp: In function 'void fast_scan(double&)':
ruins3.cpp:144:34: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
void fast_scan(double &x) { scanf("%lf", &x); }
~~~~~^~~~~~~~~~~
ruins3.cpp: In function 'void fast_scan(long double&)':
ruins3.cpp:145:39: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
void fast_scan(long double &x) { scanf("%Lf", &x); }
~~~~~^~~~~~~~~~~
ruins3.cpp: In function 'void fast_scan(char&)':
ruins3.cpp:147:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
scanf("%c", &x);
~~~~~^~~~~~~~~~
ruins3.cpp: In function 'void fast_scan(std::__cxx11::string&)':
ruins3.cpp:153:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
scanf("%s", string_in_buffer);
~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
18 ms |
26880 KB |
Output is correct |
| 2 |
Correct |
18 ms |
26880 KB |
Output is correct |
| 3 |
Correct |
17 ms |
26880 KB |
Output is correct |
| 4 |
Correct |
18 ms |
26880 KB |
Output is correct |
| 5 |
Correct |
18 ms |
26880 KB |
Output is correct |
| 6 |
Correct |
18 ms |
26880 KB |
Output is correct |
| 7 |
Correct |
18 ms |
26880 KB |
Output is correct |
| 8 |
Correct |
18 ms |
26880 KB |
Output is correct |
| 9 |
Correct |
18 ms |
26880 KB |
Output is correct |
| 10 |
Correct |
20 ms |
26880 KB |
Output is correct |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
18 ms |
26880 KB |
Output is correct |
| 2 |
Correct |
18 ms |
26880 KB |
Output is correct |
| 3 |
Correct |
17 ms |
26880 KB |
Output is correct |
| 4 |
Correct |
18 ms |
26880 KB |
Output is correct |
| 5 |
Correct |
18 ms |
26880 KB |
Output is correct |
| 6 |
Correct |
18 ms |
26880 KB |
Output is correct |
| 7 |
Correct |
18 ms |
26880 KB |
Output is correct |
| 8 |
Correct |
18 ms |
26880 KB |
Output is correct |
| 9 |
Correct |
18 ms |
26880 KB |
Output is correct |
| 10 |
Correct |
20 ms |
26880 KB |
Output is correct |
| 11 |
Correct |
72 ms |
27004 KB |
Output is correct |
| 12 |
Correct |
71 ms |
27008 KB |
Output is correct |
| 13 |
Correct |
75 ms |
26968 KB |
Output is correct |
| 14 |
Correct |
70 ms |
26880 KB |
Output is correct |
| 15 |
Correct |
95 ms |
26880 KB |
Output is correct |
| 16 |
Correct |
71 ms |
27000 KB |
Output is correct |
| 17 |
Correct |
70 ms |
27008 KB |
Output is correct |
| 18 |
Correct |
70 ms |
27000 KB |
Output is correct |
| 19 |
Correct |
70 ms |
26880 KB |
Output is correct |
| 20 |
Correct |
81 ms |
26880 KB |
Output is correct |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
18 ms |
26880 KB |
Output is correct |
| 2 |
Correct |
18 ms |
26880 KB |
Output is correct |
| 3 |
Correct |
17 ms |
26880 KB |
Output is correct |
| 4 |
Correct |
18 ms |
26880 KB |
Output is correct |
| 5 |
Correct |
18 ms |
26880 KB |
Output is correct |
| 6 |
Correct |
18 ms |
26880 KB |
Output is correct |
| 7 |
Correct |
18 ms |
26880 KB |
Output is correct |
| 8 |
Correct |
18 ms |
26880 KB |
Output is correct |
| 9 |
Correct |
18 ms |
26880 KB |
Output is correct |
| 10 |
Correct |
20 ms |
26880 KB |
Output is correct |
| 11 |
Correct |
72 ms |
27004 KB |
Output is correct |
| 12 |
Correct |
71 ms |
27008 KB |
Output is correct |
| 13 |
Correct |
75 ms |
26968 KB |
Output is correct |
| 14 |
Correct |
70 ms |
26880 KB |
Output is correct |
| 15 |
Correct |
95 ms |
26880 KB |
Output is correct |
| 16 |
Correct |
71 ms |
27000 KB |
Output is correct |
| 17 |
Correct |
70 ms |
27008 KB |
Output is correct |
| 18 |
Correct |
70 ms |
27000 KB |
Output is correct |
| 19 |
Correct |
70 ms |
26880 KB |
Output is correct |
| 20 |
Correct |
81 ms |
26880 KB |
Output is correct |
| 21 |
Runtime error |
45 ms |
54392 KB |
Execution killed with signal 11 (could be triggered by violating memory limits) |
| 22 |
Halted |
0 ms |
0 KB |
- |
